Division with rectangular multiplier supporting multiple precisions and operand types

• US 7,962,543 B2
• Filed: 06/01/2007
• Issued: 06/14/2011
• Est. Priority Date: 06/01/2007
• Status: Expired due to Fees

• Current Assignee: Advanced Micro Devices, Inc.
• Original Assignee: Advanced Micro Devices, Inc.
• Inventors: Schulte, Michael J., Tan, Dimitri, Lemonds, Carl E. Jr.
• Primary Examiner(s): Malzahn; David H
• Application Number:
  US11/756,885
• Publication Number:
  US 20080301213A1
• Time in Patent Office: 1,474 Days
• Field of Search: None
• US Class Current: 708/654
• CPC Class Codes: G06F 2207/5356 Via reciprocal, i.e. calculate reciprocal only, or calculate reciprocal first and then the quotient from the reciprocal and the numerator
• CPC Class Codes: G06F 7/4873 Dividing

Abstract

A division method includes determining a precision indicator for the division operation that indicates whether the quotient should be a single precision, double precision, or extended precision floating-point number. The division is performed at a rectangular multiplier using the Goldschmidt or Newton-Raphson algorithm. Each algorithm calculates one or more intermediate values in order to determine the quotient. For example, the Goldschmidt algorithm calculates a complement of a product of the dividend and an estimate of the reciprocal of the divisor. The quotient is determined based on a portion of one or more of these intermediate values. Because only a portion of the intermediate value is used, the division can be performed efficiently at the rectangular multiplier, and therefore the quotient can be determined more quickly and still achieve the desired level of precision.

Claims

1. A method implemented by a floating point unit of a processor, comprising:

determining a first precision indicator;

estimating a reciprocal [X₀] of a divisor to determine a reciprocal estimate;

determining a first product [D₀] based on a rectangular multiplication of the divisor and the reciprocal estimate;

determining a first complement value [R₀] based on a complement of the first product;

determining a second product [N₀] based on a rectangular multiplication of the reciprocal estimate and a dividend; and

determining a quotient of the divisor and the dividend at a rectangular multiplier based on the second product, the precision indicator, and a portion of the first complement value.

2. The method of claim 1, wherein the rectangular multiplication of the divisor and the reciprocal estimate comprises a multiply-add operation.

3. The method of claim 1, further comprising:

reducing the first complement value to determine the portion of the first complement value.

4. The method of claim 3, wherein determining the quotient further comprises:

iteratively determining a first series of products, wherein an Nth product of the first series of products is based on a rectangular multiplication of an N−

1 product of the first series of products and the N−

1 complement value of a series of complement values, the first series of products including the first product;

iteratively determining a second series of products, wherein an Nth product of the second series of products is based on a rectangular multiplication of an N−

1 product of the second series of products and an N−

1 complement value of the series of complement values, the second series of products including the second product;

iteratively determining the series of complement values, wherein the Nth complement value of the series of complement values is based on a complement of the Nth product of the first series of products, the series of complement values including the first complement value; and

determining the quotient based on a rectangular multiplication of the Nth product of the second series of products and the Nth complement value of the series of complement values.

5. The method of claim 3, wherein determining the quotient further comprises:

determining a third product based on the portion of the first complement value and the first product;

determining a fourth product based on the portion of the first complement value and the second product;

determining a second complement value based on a complement of the third product; and

determining the quotient based on a rectangular multiplication of the fourth product and the second complement value.

6. The method of claim 3, wherein determining the quotient comprises determining the quotient based on a rectangular multiplication of the portion of the first complement value and the second product in response to determining that the precision indicator indicates a single precision division.

7. The method of claim 3, wherein determining the quotient comprises:

determining a third product based on a rectangular multiplication of the portion of the first complement value and the first product;

determining a second complement value based on the third product;

determining a fourth product based on a rectangular multiplication of a portion of the first complement value and the second product; and

determining the quotient based on a rectangular multiplication of a portion of the second complement value and the fourth product in response to determining that the precision indicator indicates a double precision division.

8. The method of claim 3, wherein determining the quotient comprises determining the quotient based on a rectangular multiplication of the portion of the first complement value and the second product in response to determining that the precision indicator indicates an extended precision division of a first type.

9. The method of claim 3, wherein determining the quotient comprises:

determining a third product based on a rectangular multiplication of the portion of the first complement value and the first product;

determining a second complement value based on the third product;

determining a fourth product based on a rectangular multiplication of the portion of the first complement value and the second product; and

determining the quotient based on a rectangular multiplication of the second complement value and the fourth product in response to determining that the precision indicator indicates an extended precision division of a second type.

10. The method of claim 3, wherein determining the quotient comprises:

determining a third product based on a rectangular multiplication of the portion of the first complement value and the first product;

determining a second complement value based on the third product;

determining a fourth product based on a rectangular multiplication of the portion of the first complement value and the second product;

determining a fifth product based on a rectangular multiplication of the second complement value and the third product;

determining a third complement value based on the fifth product;

determining a sixth product based on a rectangular multiplication of the second complement value and the fourth product; and

determining the quotient based on a rectangular multiplication of the third complement value and the sixth product in response to determining that the precision indicator indicates an extended precision division of a third type.

11. The method of claim 1, further comprising:

determining a rounding control indicator; and

rounding the quotient based on the rounding control indicator.

12. The method of claim 1, wherein the precision control indicates an operand type of the dividend and the divisor.

13. A method implemented by a floating point unit of a processor, comprising:

determining a first precision indicator;

estimating a reciprocal of a divisor to determine a reciprocal estimate;

determining a first product based on a multiplication of the reciprocal estimate and the divisor;

determining a first complement value based on a complement of the first product;

determining a second product based on a rectangular multiplication of the first complement value and the reciprocal estimate;

determining a quotient of the divisor and the dividend at a rectangular multiplier based on a portion of the second product, the precision indicator, and the dividend.

14. The method of claim 13, further comprising:

reducing the second product to determine the portion of the second product.

15. The method of claim 14, wherein determining the quotient comprises determining the quotient based on a rectangular multiplication of the second product and the dividend in response to determining that the precision indicator indicates a single precision division.

16. The method of claim 15, wherein determining the quotient comprises:

determining a third product based on a rectangular multiplication of the portion of the second product and the divisor;

determining a second complement value based on the third product;

determining a fourth product based on a rectangular multiplication of the second complement value and the portion of the second product; and

determining the quotient based on a rectangular multiplication of the fourth product and the dividend in response to determining that the precision indicator indicates a double precision division.

17. The method of claim 16, wherein determining the quotient comprises:

determining a fifth product based on a rectangular multiplication of a portion of the fourth product and the divisor;

determining a third complement value based on the fifth product;

determining a sixth product based on a rectangular multiplication of the portion of the third complement value and the fourth product; and

determining the quotient based on a rectangular multiplication of the sixth product and the dividend in response to determining that the precision indicator indicates an extended precision division.

18. The method of claim 13, wherein estimating a reciprocal of a divisor comprises determining the reciprocal estimate based on a look-up table.

19. A floating point unit, comprising:

an input configured to receive a first precision indicator, a divisor, and a dividend;

a lookup table configured to provide a reciprocal estimate based on a reciprocal of a divisor;

a multiplier coupled to the lookup table and to the input, the multiplier configured to;

determine a first product based on a multiplication of the divisor and the reciprocal estimate;

determine a first complement value based on a complement of the first product;

determine a second product based on a multiplication of the reciprocal estimate and a dividend; and

determine a quotient of the divisor and the dividend based on the second product, the precision indicator, and a portion of the first complement value; and

an output configured to provide the quotient.

20. The floating point unit of claim 19, wherein the multiplier is a rectangular multiplier.